Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Analysis of emergency braking performance with particular consideration of temperature effects on brakes

During vehicle deceleration due to braking there is friction between the lining surface and the brake drum or disc. In this process the kinetic energy of vehicle is turned into thermal energy that raises temperature of the components. The heating of the brake system in the course of braking is a great problem, because besides damaging the system, it may also affect the wheel and tire, which can cause accidents. In search of the best configuration that considers the true conditions of use, without passing the safety limits, models and formulations are presented with respect to the brake system, considering different braking conditions and kinds of brakes. Some modeling was analyzed using well-known methods. The flat plate model considering energy conservation was applied to a bus, using for this a computer program. The vehicle is simulated to undergo an emergency braking, considering the change of temperature on the lining-drum. The results include deceleration, braking efficiency, wheel resistance, normal reaction on the tires and the coefficient of adhesion. Some of the results were compared with dynamometer tests made by FRAS-LE and others were compared with track tests made by Mercedes-Benz. The convergence between the results and the tests is sufficient to validate the mathematical model. The computer program makes it possible to simulate the brake system performance in the vehicle. It assists the designer during the development phase and reduces track tests.

Experimental study applied to an industrial robot by using variable structure controllers and friction compensation

Control of an industrial robot is mainly a problem of dynamics. It includes non-linearities, uncertainties and external perturbations that should be considered in the design of control laws. In this work, two control strategies based on variable structure controllers (VSC) and a PD control algorithm are compared in relation to the tracking errors considering friction. The controller's performances are evaluated by adding an static friction model. Simulations and experimental results show it is possible to diminish tracking errors by using a model based friction compensation scheme. A SCARA robot is used to illustrate the conclusions of this paper.